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10 votes
1 answer
642 views

Is the affine closure of the basic affine space of a reductive algebraic group Cohen–Macaulay?

Let $G$ be a reductive algebraic group with choices of Borel subgroup and maximal torus $B \supseteq T$ and unipotent radical $U$ over an algebraically closed field $k$ of characteristic zero. Is the ...
Tom Gannon's user avatar
3 votes
3 answers
581 views

Reductive group with simply connected derived group has all root groups $\mathrm{SL}_2$

$\DeclareMathOperator\SL{SL}\DeclareMathOperator\PGL{PGL}$Motivation: I am trying to understand why the Deligne-Langlands conjectures are only stated for $p$-adic reductive groups with connected ...
LAGC's user avatar
  • 143
3 votes
1 answer
170 views

Factoring out an element of a root subgroup to make a conjugation integral

Fix a nonarchimedean local field $L/\mathbb{Q}_p$ with ring of integers $\mathcal{O}$, uniformizer $\varpi$, and residue field $k$. If I take a matrix $$\begin{pmatrix} a & \varpi b \\ c & d \...
Ashwin Iyengar's user avatar